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On the gap between cluster dimensions of loop soups on and the metric graph of
Zhenhao Cai, Jian Ding
The question of understanding the scaling limit of metric graph critical loop soup clusters and its relation to loop soups in the continuum appears to be one of the subtle cases th…
Separation and cut edge in macroscopic clusters for metric graph Gaussian free fields
Zhenhao Cai, Jian Ding
We prove that for the Gaussian free field (GFF) on the metric graph of (for all except the critical dimension ), with uniformly positive probability…
Heterochromatic two-arm probabilities for metric graph Gaussian free fields
Zhenhao Cai, Jian Ding
For the Gaussian free field on the metric graph of (), we consider the heterochromatic two-arm probability, i.e., the probability that two points and $v'…
Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs
Zhenhao Cai, Jian Ding
In this paper, we establish the existence and equivalence of four types of incipient infinite clusters (IICs) for the critical Gaussian free field (GFF) level-set and the critical…
Quasi-multiplicativity and regularity for metric graph Gaussian free fields
Zhenhao Cai, Jian Ding
We prove quasi-multiplicativity for critical level-sets of Gaussian free fields (GFF) on the metric graphs (). Specifically, we study the probabi…